Final answer:
To find the total heat capacity of an ideal diatomic gas sample at constant volume and constant pressure, we use the molar heat capacities. For molecules that only rotate, the molar heat capacity is (5/2)R at constant volume and (7/2)R at constant pressure. If the molecules both rotate and vibrate, the molar heat capacity is (9/2)R at constant volume and (11/2)R at constant pressure.
Step-by-step explanation:
(a) To find the total heat capacity of the sample at constant volume, we can use the equation Q = nCvΔT, where Q is the heat added, n is the number of moles, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature.
For an ideal diatomic gas, Cv = (5/2)R, where R is the ideal gas constant. In this case, n = 1.70 mol and ΔT is the change in temperature.
(b) To find the total heat capacity of the sample at constant pressure, we can use the equation Q = nCpΔT, where Cp is the molar heat capacity at constant pressure. For an ideal diatomic gas, Cp = (7/2)R. Again, n = 1.70 mol and ΔT is the change in temperature.
(c) Assuming the molecules both rotate and vibrate, the total heat capacity at constant volume would include contributions from both the rotational and vibrational degrees of freedom. Cv = (5/2)R + 2R = (9/2)R.
(d) Assuming the molecules both rotate and vibrate, the total heat capacity at constant pressure would also include contributions from both the rotational and vibrational degrees of freedom. Cp = (7/2)R + 2R = (11/2)R.